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What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?

  1. A.3
  2. B.11
  3. C.12
  4. D.66
▶ Answer & Explanation

Correct answer: C. 12

When items are arranged in a circle, the concept of consecutive selection needs careful consideration of the circular arrangement. If we are selecting 10 consecutive items from 12 items arranged in a circle, we can fix the starting position of the first item in the selection. Since the arrangement is circular, moving the entire block of 10 consecutive items one position at a time will result in distinct sets of 10 items. There are 12 possible starting positions for the block of 10 consecutive items, and each starting position defines a unique selection of 10 consecutive items.

Source: UPSC csat 2023

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